The determination of the strain in GaAs/Ga_xIn_1–xAs strained-layer structures from measurements of thickness fringe displacements

Abstract

The initial stage in the development of a technique which has the aim of determining the misfit strain in structures containing strained layers is described. The method is applied to a GaAs system containing Ga _x In_1-x As strained layers. Transmission electron microscopy images of the shifts in the thickness fringes in {100} epitaxial layers due to strain relaxation at the edge of 90° wedge samples are matched to simulated images obtained by calculating the strain relaxation and solving the equations for the two-beam dynamical theory of diffraction contrast. The simulated images are analysed as a function of the deviation parameter s, the misfit strain f, the g vector, the extinction coefficient ζ _g and the anomalous absorption coefficient ζ _g . The simulated images are sufficiently sensitive to f and to s that contrast patterns can be distinguished which differ by less than 0–02% in f and by about 1 × 10⁻⁴ Å⁻¹ in s. The pattern of the image is not very sensitive to changes in ζ _g or ζ _g . Thus the pattern matching of experimental and simulated images leads to values of s and f only. The sensitivity both to s and to f is illustrated by examining a single strained Ga_0·8In_0·2As quantum well with GaAs barriers. The values for the misfit strain obtained are in good agreement with expected values from growth and photoluminescence measurements. The results also indicate a rotation of the cap with respect to the substrate and a slight relaxation of the strain due to misfit dislocations.